Emergent superconductivity in topological-kagome-magnet/metal heterostructures

Itinerant kagome lattice magnets exhibit many novel correlated and topological quantum electronic states with broken time-reversal symmetry. Superconductivity, however, has not been observed in this class of materials, presenting a roadblock in a promising path toward topological superconductivity. Here, we report that novel superconductivity can emerge at the interface of kagome Chern magnet TbMn6Sn6 and metal heterostructures when elemental metallic thin films are deposited on either the top (001) surface or the side surfaces. Superconductivity is also successfully induced and systematically studied by using various types of metallic tips on different TbMn6Sn6 surfaces in point-contact measurements. The anisotropy of the superconducting upper critical field suggests that the emergent superconductivity is quasi-two-dimensional. Remarkably, the interface superconductor couples to the magnetic order of the kagome metal and exhibits a hysteretic magnetoresistance in the superconducting states. Taking into account the spin-orbit coupling, the observed interface superconductivity can be a surprising and more realistic realization of the p-wave topological superconductors theoretically proposed for two-dimensional semiconductors proximity-coupled to s-wave superconductors and insulating ferromagnets. Our findings of robust superconductivity in topological-Chern-magnet/metal heterostructures offer a new direction for investigating spin-triplet pairing and topological superconductivity.


Supplementary Text III
The surface superconductivity with s-wave pairing symmetry in the quantum-limit Chern topological magnet TbMn 6 Sn 6 1 induced by a strong Rashba type SOC is proposed to explain the observed interface superconductivity, considering that the superconductivity takes place in the Kagome layer with the strong exchange coupling.
The interplay between the topological band structure on the (001) surface and the swave pairing may lead to p-wave-like topological superconductivity.This Rashba-type SOC originates from the electric field induced by the strong structural inversion asymmetry on the surface 2 .Experiments and numerical simulations have proved the large Rashba SOC on the surface of Au 3,4 as well as the interface between ferro-and non-magnetic materials 5 .The effective Hamiltonian  16a).  is the coupling strength of the Rashba-type SOC.
When s-wave superconductivity is induced, the superconducting pairing parameter Δ = 1.In the absence of superconductivity and Rashba-type SOC, the system is in a quantum anomalous Hall state, and chiral edge states are present (Supplementary Fig. 16b).Since the system is spin-polarized, the formation of conventional s-wave superconductivity is hampered.When Rashba-type SOC is introduced, the spin-up

Supplementary Text IV
As discussed in Supplementary Text II, the TbMn 6 Sn 6 sample near the interface has a naturally formed degraded layer possessing polycrystalline TbMn 6 Sn 6 .When we consider the Kagome structure in the degraded TbMn 6 Sn 6 layer, the interplay between the topological band structure on the (001) surface and the s-wave pairing could also lead to effective p-wave topological superconductivity.This Rashba-type SOC originates from the dramatic structural inversion asymmetry on the degraded layer shown in Fig. 4  connect neighbor sites i and j (Supplementary Fig. 17a).  is the coupling strength of the Rashba-type SOC.
Hereinbelow, considering the weaker effective exchange coupling strength in the degraded interface layer, we set t = 1, J = 0.75,    and  = 0.1 with the arbitrary unit.When s-wave superconductivity is induced, the superconducting pairing parameter Δ=0.5.In the absence of superconductivity and Rashba-type SOC, the system is in a quantum anomalous Hall state.Since the system is spin-polarized due to the exchange coupling, the formation of conventional s-wave superconductivity is hampered.When Rashba-type SOC is introduced, the spin-up and spin-down components of the electrons are mixed as shown in Supplementary Fig.
and spin-down components of the electrons are mixed.The formation of conventional s-wave superconductivity becomes possible and leads to a pairing term to the total Hamiltonian: ℋ   , where  Δ ∑  ↑  ↓ Δ * ∑  ↓  ↑ .By calculating the BdG Chern number N 6,7 , we summarize the phase diagram in terms of  and  in Supplementary Fig. 16c.The system can enter into the chiral topological superconducting phase with N = 1.We take a typical value  2 and increase  , the BdG band is shown in Supplementary Fig. 16e and 16f, where a pair of chiral Majorana modes emerge around E = 0. Furthermore, as shown in Supplementary Fig. 16d, the effective superconducting gap ∆ is enhanced by increasing  and can be suppressed by the finite temperature in real experimental conditions.Therefore, a large Rashba SOC is necessary to host the superconductivity with the BdG Chern number N = 1 (ref.7).
17b.The formation of conventional s-wave superconductivity becomes possible and leads to a pairing term to the total Hamiltonian: ℋ   , where  Δ ∑  ↑  ↓ Δ * ∑  ↓  ↑ .By calculating the BdG Chern number N 6,7 , we summarize the phase diagram in terms of  and  in Supplementary Fig. 17c.The system can enter into the chiral topological superconducting phase with N = 1 near  3, which lies in the original topological flat band of the lower magnetic sub-band.We take a typical value  3.2 and increase  , the BdG band is shown in Supplementary Figs.17e and 17f, where a pair of chiral Majorana modes emerge around E = 0. Furthermore, as shown in Supplementary Fig. 17d, the effective superconducting gap ∆ is enhanced by increasing  and can be suppressed by the finite temperature in real experimental conditions.Therefore, a large Rashba SOC is necessary to host the superconductivity with the BdG Chern number N = 1 (ref.7).
1of the system with Rashba type   , with hopping  and chemical potential . is the effective exchange coupling strength.  /√     •  and    are the parameters of the Kane-Mele type SOC.  represent the bond unit vectors that connect neighbor sites i and j (Supplementary Fig. (ref. 2).The effective Hamiltonian 1 of the system with Rashba-type   , with hopping  and chemical potential . is the effective exchange coupling strength.  /√     •  and    are the parameters of the Kane-Mele type SOC.  represent the bond unit vectors that